I would lean toward the booster being the problem. If it is a rebuilt unit there may be a fault in it. You must also check the actuating shaft that goes through the firewall. Insure that the shaft itself is not binding. If it is that could mean the booster is not in proper alignment with the shaft or it is incorrect for your application. A sticking caliper should never affect the pedal.
Next time it sticks try pulling up from under it with your left foot. That may give you an indication as to where the bind is. - Bill